Question
Show that the photons in a $1240-\mathrm{nm}$ infrared beam have energies of $1.00 \mathrm{eV}$.
Step 1
Step 1: First, we need to recall the formula for the energy of a photon, which is given by: \[E = \frac{hc}{\lambda}\] where \(h\) is Planck's constant, \(c\) is the speed of light, and \(\lambda\) is the wavelength of the light. Show more…
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Show that the photons in a 1240 -nm infrared beam have energies of $1.00 \mathrm{eV}$ $$ \mathrm{E}=h f=\frac{h \mathrm{c}}{\lambda}=\frac{\left(6.63 \times 10^{-34} \mathrm{~J} \cdot \mathrm{s}\right)\left(2.998 \times 10^{8} \mathrm{~m} / \mathrm{s}\right)}{1240 \times 10^{-9} \mathrm{~m}}=1.602 \times 10^{-19} \mathrm{~J}=1.00 \mathrm{eV} $$
Show that the wavelength $\lambda$ in $\mathrm{nm}$ of a photon with energy $E$ in $\mathrm{eV}$ is $\lambda=1240 / E.$
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